Electromagnetism problem (with polarization)

[Penny_bang]

Hello everybody. I have a big problem (it is not a homework but an important exercice) which i can't solve and i have no solution ...

A circularly polarized monochromatic wave is reflected from a dielectric mirror which has parameters μ and ε. Its wave vector is k = (k0, 2k0,0). Find the magnetic field B, the electric field E and the Poynting vector S as well as the angle of incidence for which the reflected wave is linearly polarized (i.e. the Brewster angle). Calculate the energy of the system.

 

I think we have to use this (very) general equations :

B = B0.sin(ωt + δ)

rot E = - ∂B/∂t

E = -ωB0.cos (ωt + δ)

where : ω=k.c = 2∏c/λ

For the circular polarization, the electric field rotates about its axis in a circle.

Then, for linear polarization: E remains in the same plane.

For the Poynting vector : S = B x E / μ (i am not sure if for this equation i have to use μ or μo (in vacuum)). Then we can calculate the energy, I guess ...

About the angle Brewster, i think we have to use the Fresnel equations (but i don't know how ...).

I wonder whether it would be better to use the equations in the complex form (instead of the actual form equations (real form)). I don't know how establish reflection equations for different polarizations, and how resolve circular polarization into components with the plane of the mirror

 

Can you help me, please ? Thank you in advance.

I know that what i have written is not very usefull ... And I'm sorry. I really would like to know how to begin at least.